public housing is a part of the picture, and so are public libraries. The solution is certainly not to cut library spending just because there are homeless people using it
Thinking there being homeless people around is an issue that needs solving is itself pretty bigoted. Like, maybe you have a problem with people who haven't showered for a while? or people who use the library for personal activities because there are no better places for them to do them? But 'these people are a problem' itself becomes problematic because you've consolidated those qualities you find objectionable into a class of person, and that makes it really easy to forget/misplace/dismiss the humanity those people deserve.
It's a common attitude, so don't feel like i'm picking you out personally to scold. More people should be aware of how that attitude dehumanizes people experiencing shelter insecurity.